Evaluation of inhibitive corrosion potential of symmetrical hydrazine derivatives containing nitrophenyl moiety in 1M HCl for C38 steel: experimental and theoretical studies

The exploitation of cost-effective, sustainable, green and efficient compounds is a renewed science and a demanding mission for today's chemists and technologists. In this view, the inhibitive corrosion properties of some hydrazine derivatives named (1E,2E)-bis(1-(2-nitrophenyl)ethylidene)hydrazine (SSBO), (1E,2E)-bis(1-(3-nitrophenyl)ethylidene)hydrazine (SSBM) and (1E,2E)-bis(1-(4-nitrophenyl)ethylidene)hydrazine (SSBP) on the C38 steel corrosion in 1M HCl media has been evaluated by different techniques like electrochemical impedance spectroscopy (EIS), potentiodynamic polarization (PDP), scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy. The EIS results showed that SSBM is the greatest inhibitor (η>93%) among the three tested compounds. The SSBM gives considerable inhibition efficiency against corrosion of steel compared to the previous studies. The PDP curves indicated that the studied inhibitors were a mixed-type inhibitor with a predominantly cathodic control. Quantum calculations of some descriptors derived from the density functional theory (DFT), the transition state theory (TST), the quantum theory of atoms in molecules (QTAIM) and molecular dynamics simulation have delivered helpful information regarding electron transfer and mechanism during adsorption of inhibitors on C38 steel surface.


Introduction
C38 steel is a material extensively used in many engineering domains, which due to its low cost and high availability for the building of several industrial materials [1]. The foremost problem of applying C38 steel in the industry is its destruction in different aggressive environments, particularly in acidic solutions [2]. Unfortunately, acid solutions are frequently used in industry for cleaning, descaling, oil-well acidifi- growing electrical resistance of the metal [6,7]. Additionally, most organic inhibitors that were used against corrosion can be adsorbed on the metal surface via e-poor and/or e-rich sites such as heteroatoms, unsaturated bonds or aromatic rings, lone-pair and/or electrons, orbitals *, reactive functional groups, and inversely charged sites relative to the charged metal surface [8,9]. Nowadays, innovative studies are going on for the sustainable ecosystem development of so-called "ecofriendly" corrosion inhibitors by the use of efficient and inexpensive compounds with a weak or nothing negative environmental impact [7].
In view of these recommendations we have exploited some symmetrical hydrazine derivatives containing nitrophenyl moiety, namely (1 ,2 )-bis(1-(2-nitrophenyl)ethylidene)hydrazine (SSBO), (1 ,2 )bis(1-(3-nitrophenyl)ethylidene)hydrazine (SSBM) and (1 ,2 )-bis(1-(4-nitrophenyl)ethylidene)hydrazine (SSBP) to explore their inhibitive corrosion properties for C38 in molar hydrochloric solution using electrochemical impedance spectroscopy (EIS), potentiodynamic polarization (PDP), and surface analysis using scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDS) and element mapping via electronic-microscopy horizontal scanning test (EM). Then, quantum calculations based on the density functional theory (DFT), quantum theory of atoms in molecules (QTAIM), molecular electrostatic potential surface (MEP) analysis, transition state theory (TST) and molecular dynamics (MD) simulation were achieved. These three theoretical approaches have been proven to be very effective in finding new physic-chemical information on the adsorption mechanism. These theoretical studies allow investigating and establishing a relationship between the efficiency of corrosion inhibition of the SSBs compounds (i.e., SSBO, SSBM and SSBP) and the electron density distributed within each one of them. Also, these techniques will give more information regarding the effect of nitro group on molecular structure behavior of three compounds (SSBs) presented in Fig. 1. Previously studies were carried about inhibitive corrosion of other hydrazine derivatives which showed inhibition efficiency ranged from 62.40 to 86.70% at optimum concentration of 1mM in molar hydrochloric acid [10,11,12]. One compound of our tested hydrazine molecules gives best inhibition efficiency of 93.04% at the same optimum concentration.
The choice of these hydrazine derivatives (SSBs) to test their anticorrosive properties is based on the following cautions (a) their synthesis process easy and not expensive, (b) they are formed with high yield, (c) have many biological activities and excellent fluorescent chemosensors for metal ions [13], (d) they are no poisonous, (e) contain heteroatoms (N and O), (f) contain ortho-, meta-or para-nitro group (with electron-withdrawing) leading to the partial charges on carbon chain of aromatic ring, (g) they are -conjugated systems with 2,3diaza group (R-C=N-N=C-R), (h) possess methyl group (with electrondonor) which ensure availability of electron density around nitrogen atoms of 2,3-diaza group, (i) they are symmetrical systems [13,14]. The considerations (d), (e), (f), (g), (h) and (i) offer the studied compounds a high ability to form covalent or/and non-covalent bonds with C38 steel and thus forming a protective layer against corrosion. According to an extensive bibliographic study, until this date, no work has been done on these compounds as corrosion inhibitors.

Inhibitors
The tested hydrazine derivatives (SSBs) were resynthesized with high yields according to the protocol defined in the following reference [14]. All details about the characterization of SSBs products are defined in the same reference. The molecular structure, acronyms and IUPAC names of concerned compounds are given in Fig. 1.

Electrochemical experiments
Electrochemical tests were performed using a potentiostat PGZ101 and a three-electrode cell, controlled by a computer machine equipped with Voltamaster4. The CS, the platinum and the electrode with saturated calomel Ag/AgCl/KCl (SCE) are used respectively as working electrode, counter electrode and reference electrode. The electrochemical tests were carried out in 1M HCl solution without and with different concentrations of inhibitor (0.05 mM, 0.1 mM, 0.5 mM, and 1 mM). Nyquist and Bode curves were plotted after the 1 hour immersion in the corrosive solution in the absence and in the presence of different concentrations of the inhibitor using an Ac signal with amplitude of 10 mV peak to peak and a frequency range of 100 kHz to 10 mHz [8]. Equivalent circuit was obtained by the fitting of the experimental curves using Ec-Lab software. The PDP curves were logged from −800 to −100 mV at a scan rate of 0.5 mV/s [8]. To guarantee the reproducibility of electrochemical results, all EIS and PDP measurements were repeated three times. The Ec-Lab10. 36 and OriginPro8 software were used to analyze results from EIS and PDP. The fitting errors did not surpass 10% and the 2 was below 10 −3 .

Surface characterization
The pre-treated CS surface was analyzed before and after its emersion in acidic media in the presence and absence of 1mM of SSBs for 24 hours at 308 K with digital microscope imaging TESCAN model equipped with a chemical analysis system with an accelerating voltage of 15 kV allowing penetration of the electron beam into the material and leading to the realization of extreme surface chemical analysis.

Quantum calculation details
Full geometry optimizations of all structures were carried out using the DFT theory and the B3LYP functional coupled together to the 6-311G+ +(2d,2p) basis set for the following atoms H (hydrogen), C (carbon), N (nitrogen) and O (oxygen). However, for the iron atoms (Fe), the basis set 6-311G + +(2d,2p) was replaced by another one that is more appropriate its name is abbreviated as LanL2DZ. All DFT calculations were achieved under an implicit solvation model (SMD) using Gaussian 09 Revision D-01 [15,16]. The DFT, QTAIM, MESP and TST theories were used to give more supplementary information regarding the molecular structure of inhibitor and confirm the results obtained experimentally. Several quantum chemical descriptors that indicate structural characteristics of organic inhibitors (SSBs and SSBH +), such as E HO(inh) (energy of the highest occupied molecular orbital), E BV(inh) , (energy of the lowest unoccupied molecular orbital), Fermi level energy (FEL) of Fe(110) and so on, were obtained [17]. DFT also provides a convenient theoretical framework for calculating global and local indices that describe chemical reactivity of chemical species quantitatively. The energy gap (ΔE (inh) ), energy gap (ΔE (inh-Fe) ), chemical potential , electronegativity ( ), chemical hardness ( ) and chemical softness ( ), which make it possible to evaluate the tendency of an atomic site to acquire electrons, these descriptors are calculated using the following equations (1)-(5), respectively [18]. Therefore, the electrophilic index ( ) is a popular quantum descriptor that defines the capacity of a compound to receive electrons from an acceptor chemical species. The descriptor can be calculated by the following equation (6) [18]. Besides, the flow of electrons (ΔN (110) ) moved from (to) the inhibitor to (from) the metal surface was calculated according to the following equation (7).
The active sites existing in an organic molecule of inhibitor are determined by analyzing the local reactivity indices such as Parr functions − (electrophilic attack) and + (nucleophilic attack) based on the Mulliken atomic spin density (MASD) calculations [19] and using Fukui functions − and + calculated in terms of natural population analysis (NPA). The high value of + or + measures the change in electron density at an atomic site when the molecule belongs to receive an extra electron and − or − measures the change in electron density at an atomic site when the molecule belongs to has lost an extra electron. The local reactivity was also evaluated basing on the HOMO and LUMO shapes, molecular electrostatic potential surface (MEP) and non-shared electron density (NSED), which calculated according to the quantum theory of atom in molecules (QTAIM) [20,21,22]. Moreover, in order to contribute more understanding of the local reactivity associated with the studied molecules, dual local functions that are defined for an atomic site k as dual local Fukui Δ (the local nucleophilic Fukui index − minus electrophilic Fukui index +), dual local softness Δ (the nucleophilic local softness − minus the local softness +), and the philicity Δ (the local nucleophilic index − minus the local electrophilic index +) are calculated and discussed [18].
To investigate non-covalent interactions (NCI) which can characterize inhibitor structure, an empirical dispersion GD3 scheme by Grimme was added to the B3LYP functional at DFT theory [23,24]. Unlike B3LYP, the corrected functional B3LYP-GD3 appears to be reliable for investigating non-covalent interactions [23,24]. The NCI calculations were performed using Multiwfn and VMD software [25]. In quantum chemistry, the NCI theory aimed to visualize qualitatively non-covalent interactions in 3D dimensions of the molecular space. Therefore, the visual NCI depiction arises from the isosurfaces of the reduced density gradient which is colored by a scale of strength defined as follows: strong attractive interactions (blue), weak interactions (green) and strong repulsive interactions (red). The gradient is expressed as a function of the electron density (r) according to the following equation (8) [25]: The frequency calculations of the stationary points were displayed to verify the number of imaginary frequencies (zero for global minima and one for TSs) [26]. The TSs of the corresponding complexes "inhibitor⋯Fe" were localized using transition state theory on the basis of second-order Gonzalez-Schlegel integration quadratic synchronous transit-guided quasi-Newton (QST2) approach using both B3LYP and B3LYP-GD3 functional at DFT method [27,28]. The localization of TSs structures is subsequently followed by analysis IRC (intrinsic reaction coordinates (IRC) in order to check the energy profiles connecting each TS to both associated minima (reagents and products) [19,29]. The global electronic density transfer (GEDT) at the TSs was calculated by the sum of the natural atomic charges (Q) of the atoms belonging to both donor (Q > 0) and acceptor (Q < 0) fragments (F) characterized the TSs structures. The direction of the electron density flux takes place from the donor fragment to the acceptor fragment one [30,31].
The strength of coordination between active sites of inhibitor and iron atoms was evaluated by analyzing calculating the electronic configurations and calculating the second-order stabilization energy E (2)  , the E (2) energy, which is associated with the electron density delocalization between donor and acceptor (i→j), is estimated by the following equation (9) [32]: where q i is the orbital occupancy, i , and j are NBO diagonal elements (orbital energies), and F ij is the off-diagonal NBO Fock matrix element.

MD simulation methodology
Pre-optimization of Fe (110) surface was carried using generalized gradient approximation (GGA) in the Dmolˆ3 module with the polarization function DNP+ implanted in Material Studio 2016 (MSv.8.0) software package [33]. The simulation of the chemical species such as SSBs, 20 Chloride ions (20Cl-), 5 oxonium ions (5H3O +) and 500 water molecules (500 H2O) was carried out on a supercell containing 6 layers of iron atoms using forcite module integrated into MSv.8.0 software package. The calculation parameters for the MD simulations are gathered in Table 1 [33].

EIS measurements
Nyquist and Bod representation of EIS plots for CS in 1M HCl without and with inhibitor at various concentrations are shown in Fig. 2 and 3, respectively. As shown in Fig. 2, the loops are not perfect semicircles which indicate that the three compounds develop a non-perfect layers; this behavior can be attributed to the frequency dispersion, which is due to the roughness and inhomogeneity of the CS surface [8]. Furthermore, in the uninhibited solution, we note the appearance of a single capacitive loop, whereas in the presence of inhibitor, the shape and size of the Nyquist traces are different. Indeed, they present two superimposed capacitive loops. At high frequency a first capacitive loop was attributed to the formation of a film barrier by the inhibitor on the CS surface, while the second at low frequency was related to the charge transfer capacity [13,34]. This result was confirmed through the analysis of Bode plots (presence of two-time constants) Fig. 3. Note that all three SSBs compounds exhibited the same electrochemical behavior exhibited the same electrochemical behavior. The equivalent circuit shown in Fig. 4 is used for modeling of impedance spectra of SSBs on C38 steel surface [35,36]. The circuit is composed of solution resistance ( ), inhibitor film resistance ( ), charge transfer resistance ( ), and two constant phase elements such as the constant phase element of the double layer capacity (CPE ) and inhibitor film constant phase element (CPE , ) [8]. The constant phase element (CPE) is usually used to take into account the inhomogeneity on the metal surface and to fit the Nyquist depressed semicircles more accurately. The calculated impedance parameters from the equivalent circuit are collected in Table 2. The inhibition efficiency (%) of the tested inhibitors and the surface coverage was calculated using the given equations (10) and (11) [8].
In this case, = + , and blanck , inh respectively represent the polarization resistance without and with the inhibitor. The CPE is expressed by the following equation (12) [8]: In the above equation, is the amplitude comparable to a capacity, 2 = −1, the angular frequency and n is the inhomogeneity parameter (−1 < < 1) where n = 1 and n = −1 the CPE corresponds, respectively to a capacitor and an inductance, while if = 0 the CPE is equivalent to a pure resistance and when = 0.5 refers to the Warburg impedance [8].
The capacity of the double layer (Cdl) was given by the following relationship (13) [10]: Table 2 shows an increase in film resistance and charge transfer resistance with increasing inhibitor concentration, inducing the increase  of polarization resistance ( ) values and inhibitory efficiency. The increase in film strength reveals the formation of a thin film by adsorption on the metal surface. The formed film can be considered as a physical barrier that protects the CS surface from corrosion [8]. This is manifested, on the one hand, in the increase of the charge transfer resistance and, on the other hand, in the decrease of the element and the double layer capacity . This is explained by the increase of the thickness of the organic deposit with the adsorption of the inhibitor molecules; hence the decrease of the capacity of the double layer . Knowing that, the is inversely proportional with the organic deposition thickness by the Helmotz relation (14) [8].
where is the thickness of the protective layer, dielectric constant of the medium, 0 the vacuum permittivity, and is the effective surface area of the electrode [10]. According to Table 2, the addition of inhibitor leads to a noticeable increase of the inhomogeneity parameter " " for two inhibitors SSBM and SSBP. Similarly, by the addition of the SSBO inhibitor, the n parameter increases slowly compared to the n values obtained for the white solution. This result indicates that the CS surface homogeneity improved significantly by the addition of SSBM than SSBP and SSBO. However, even though the three tested compounds present acceptable inhibitive efficiencies, we can note that in the case of the ortho-and para-positions of the nitro group, the corresponding compounds (SSBO and SSBP) have relatively low inhibition efficiency compared to that where the nitro group in the meta-position (SSBM). As previously described, this could be attributed to the hydrogen bonding C-H⋯N and -bonds interactions in the case of meta-position whereas the threedimensional distance is not helpful to the formation of hydrogen bonding and/or -bonds interactions in the case of ortho-and para-positions [13].

Stationary measurements
Polarization plots of CS in 1M HCl without and with inhibitor at different concentrations are given in Fig. 5. PDP data such as corrosion potential ( corr ), corrosion current density ( corr ), Tafel coefficients cathodic ( ) and anodic ( ) and inhibition efficiency (%) are gathered in Table 3. The inhibition efficiency of (%) was calculated according to the following equation (15) [8]: where corr and ℎ are the corrosion current density without and with inhibitor, respectively. The addition of the inhibitors SSBs leads to a remarkable decrease in the current density with a displacement of the corrosion potential to negative values for all concentrations with a maximum shift not exceeding ±85 mV. This result indicates that the SSBs molecules behave more towards the reactive cathodic sites by delaying the reduction reaction of H+ ions. The anode branch is also affected by the addition of SSBs but to a lesser extent, which suggests that the SSBs molecules could also reduce the anodic dissolution of CS [8]. This behavior could be explained by the adsorption of SSBs molecules on CS surface and inhibits the dissolution of this metal.

Adsorption isotherm
Surface coverage for different concentrations of inhibitor are graphically tested to allow fitting of a proper adsorption isotherm. Some isotherms (Temkin, Frumkin and Langmuir isotherm) have been tested [37]. The results indicate that Langmuir isotherm is the best model that expresses the adsorption behavior of the studied interfaces. The Langmuir adsorption isotherm is given by the following equation (16) [37]: where C inh , , and K ads are the inhibitor concentration, surface coverage degree, and the equilibrium constant of adsorption process, respectively.  C inh / plotted versus C inh for SSBs which gives a straight line (Fig. 6).
Free energy of adsorption Δ ads can be calculated as follows (17): with R is the perfect gas constant equal 8.314 J.mol −1 .K −1 , T is the temperature equal 308 K and K ads is the inverse of the intercept of the plot. The decimal number 55.5 defines the concentration of water in mol.L −1 [38]. The values of Δ ads and ads are grouped in Table 4.
The calculated values of ΔG ads are −36.052, −38.741 and −38.399 kJ.mol −1 for SSBO, SSBM and SSBP, respectively. Generally, the large negative extent of ΔG ads showed the adsorption progress and strength of protective layer on CS surface [37]. Values of ΔG ads around −20 kJ.mol −1 are reliable with physisorption and those around −40 kJ.mol −1 or higher are associated with chemisorption which due to the sharing and/or electron density transfer between organic molecules of inhibitor and CS metal [39]. In this case, the calculated ΔG ads values for SSBs are ranging between −36.052 and −38.741 kJ.mol −1 , suggesting that the adsorption of SSBs on CS surface in 1M HCl solution is both physisorption (electrostatic interactions) and chemisorption (strong interactions) [40]. Actually, it can be concluded that SSBs can adsorb on the CS surface in two different manners: (i) The SSBs molecules electrostatically adsorb onto the anions enclosed CS surface via its protonated form (ii) the SSBs molecules contend with chloride ions for places at the water surrounded CS surface and the unbounded electron density of nitrogen and oxygen atoms may be reacted with the empty-d orbitals of C38 steel to form a barrier film against corrosion.  (Fig. 7b). In contrast, the CS surface remained undamaged noticeably by the addition of two inhibitors SSBM and SSBP as shown in Fig. 7c and 7d, respectively. This result can be attributed to the high capability of these inhibitors to form a better protective film entire CS surface that prohibits the migration of ionic liquid (H 2 O, Cl − ) to the surface. Further, we noticed that SSBO is not contributing more to the enhancement of CS surface with respect to the SSBM and SSBP. As for SSBP, in spite of it improves the corroded surface of CS, its efficiency remains less compared to that of SSBM. So, henceforth the addition of SSBM inhibitor would be the real solution to protect CS surface from acidic corrosion. The presence of some elements that adhered CS surface was investigated using EDS (Fig. 7f-7j) and element mapping analysis (Fig. 8a-8d). Furthermore, it might be gotten that EDS spectra obtained of CS in corrosive media (1M HCl) shown the presence of some atoms such as iron (92.21%), carbon (0.38%), oxygen (4.17%), and chlorine (1.43%). This result shows clearly the decrease in the amount of iron and apparition of new oxygen atoms (4.17%) and chlorine (1.43%) on the uninhibited CS surface which indicates its attachment with acidic solution content; and thus the dissolution of a part of iron in acidic solution. This is in accordance with the observations investigated from element mapping analysis ( Fig. 8a-8b). However, the addition of the SSBs does not vary the WT% of carbon obtained for abraded CS surface; in contrast, we noticed an apparition of oxygen atoms with a low weight percentage (1.22 W% for SSBM and SSBP and 1.13% for SSBO) compared to that obtained for uninhibited CS surface and new atoms of nitrogen with 1.22% for SSBM and SSBP and 1.13% for SSBO. It is also noted that the WT% of carbon atoms is almost unchanged by the addition of the inhibitor. So far, the confirmation of which inhibitor atoms can adhere to the CS surface seems unclear across EDS spectra. According to the element mapping graphs, we noticed that the number of oxygen atoms is highly increased when the inhibitor was added; while for the carbon atoms is slightly increased. As well we perceived an important amount of nitrogen atoms adhere to the CS surface. This result suggests that inhibitor molecules interact with the CS surface with their oxygen atoms of nitro groups and nitrogen atoms of 2,3-diaza group to form a protective film on the fully concerned surface. Additionally, we noticed well that the iron mapping obtained by the addition of SSBM and SSBP are almost the same as abraded CS surface. Similarly, we noticed that the addition of SSBO does not regenerate perfectly the iron mapping image of abraded CS surface that is considered as a reference sample. This confirms the follow trend of inhibition efficiency: SSBM > SSBP > SSBO.

Global reactivity behavior (GRB)
It is commonly recognized that the interaction between inhibitor and metal surface depends on the E HO and E BV levels of inhibitor molecule and the FEL of metal. The studied SSBs molecules differ from one another by the presence of the nitro group in different positions (ortho, meta or para), which probably change the electronic properties of these molecules. E HO and E BV for SSBs, and FEL for bulk iron surface (110) (supercell of 14*14) are shown in Fig. 9. Table 5 exposes the QCDs descriptors like E HO , E BV , FEL, ΔE (inh) , ΔE (inh-Fe) , , , and ΔN. Except ΔE (inh-Fe) descriptor, all other descriptors have been investigated the following trend of the corrosion inhibition efficiency as: SSBP < SSBO < SSBM, which is in disagreement with the experimental results. Otherwise, it must be noticed that some researchers discovered that ΔE (inh) descriptor cannot forthrightly predict the experimental order of inhibitive performance related to the inhibitor molecules [17]. As for ΔE (inh-Fe) , its low value causes the growth of inhibitor molecules on the metal [17]. The calculated ΔE (inh-Fe) values are 6.207, 5.485 and 5.745 eV for SSBO, SSBM, and SSBP, respectively. In this case, the trend of the corrosion inhibition efficiency (SSBM > SSBP > SSBO) for the three studied inhibitors is well in agreement with its inhibitory efficiency observed experimentally. Furthermore, electron-donating and or electron-accepting capability related to these inhibitors can also be evaluated based on the fraction of electrons transferred (ΔN) between metal substrate and inhibitor molecules (Table 5). In fact, it was pointed out that the value of ΔN is positive and less than 3.6 indicates that the studied inhibitors act as electron donors.

Local reactivity behavior (LRB)
To determine the active centers of the inhibitor molecules, nucleophilic Parr functions − (electrophilic attack) and + (nucleophilic attack), QTAIM indices, HOMO/LUMO isosurfaces and molecular electrostatic potential surface (MEP), as well as local dual descriptors like dual Fukui (Δ ), dual local softness (Δ ) and the dual local philic-ity (Δ ) were considered and discussed. Moreover, QTAIM calculations give a clear view regarding e-poor and e-rich sites of a molecule. This calculation aimed to describe non-shared electron density (NESD) around atomic site of inhibitor molecule based on the delocalized and localized index measurements. So, regarding the adsorption process, atomic sites on a molecule with a high value of + or enough value of NESD behave like nucleophilic atomic sites when they react with iron atoms' surface to form covalent bonds. Also, atomic sites with a high value of − or not enough value of NESD may be responsible for forming coordination bonds by accepting electron density from the metal. Generally, the atomic centers with a negative or negligible value of Parr indices are considered as not active centers. QTAIM analysis  is widely exploited to make clear the non-covalent interatomic interactions in a molecular system, by calculating the electron density that circulates within the molecular system. The analysis of HOMO/LUMO and MEP maps was performed and given in Fig. 10. Parr and QTAIM indices calculated for main atoms of the SSBs (Table 6 and Fig. 11).  Based on the QTAIM analysis results, we noticed for three studied inhibitors a high electron-donor activity of nitrogen atoms N3 and N4 (very enough values of NSED >2e) and oxygen atoms O5, O6, O7, and O8 (very enough values of NSED >4e). This result is confirmed by MEP plots analysis which presents strong electron density at these atoms (regions with red color) (Fig. 10). These atomic centers act as electron-donor centers when they interact with the empty-3d orbitals of the iron surface to form coordinate bonds. On the other hand, some carbon atoms of the aromatic ring and methyl groups, and some hy-  drogen atoms that carry low negative electron densities (regions with yellow color) are also attacked by electrophilic centers through electrostatic interactions. According to Fig. 10, we have observed also that the electronic density (HOMO) is very located on 2,3-diaza group containing nitrogen atoms (N3 and N4) for the two inhibitors (SSBM and SSBP) and on the nitro groups for the SSBO. While, for the electronic densities (LUMO) are low located on both aromatic ring surface and nitro groups for the three studied inhibitors. This indicates that these inhibitors have the high ability to give electrons to the metal surface (high density of HOMO) and low capability to accept electrons from the metal surface (low density of LUMO). Regarding the present case of adsorption, the high value of − on any atom present in the inhibitor molecule indicates that the atom prefers to coordinate with the iron surface according to the electron-donating process. As can be observed in Table 6 and Fig. 11, − values of electron-donor atoms of three studied inhibitors have increased as follows: −(SSBM) > −(SSBP) > −(SSBO); this order is in parallel with inhibitory efficiency of inhibitors evidenced experimentally.
In addition, to provide more insights about local reactivity, Δ , Δ and Δ are calculated. Their corresponding equations (18)- (20) are as follows [41,42]: It was described that if these descriptors are less than 0, the affected site is favored for an electrophilic attack. While if these descriptors are greater than 0, the affected site is favored for a nucleophilic attack. The results of Fukui functions ( + and − ), the local softness ( + and − ), the local electrophilicity ( + and − ), the dual Fukui function (Δ ), the dual local softness (Δ ), and the dual local philicity (Δ ) are reported in Table 7. Furthermore, the results of the dual local softness and the dual local philicity are analyzed and discussed for the most active sites of molecules studied. A schematic illustration of the dual local descriptors is given in Fig. 12. From Table 7, the three dual local descriptors calculated for SSBM and SSBP are higher than zero for the following sites (N1, N2, N3, N4, O5, O6, O7, O8, C9 and C10), which indicate that both SSBM and SSBP have many active centers that have the ability to give electrons to the metal surface. While, it is observed that all carbon atoms of the two aromatic rings have dual local descriptors lower than zero, suggesting the presence of the electrophilic character of the active sites around the SSBM and SSBP molecules. As shown in Fig. 12, the most active sites for electron-donating centers for SSBM and SSBP have almost the same trend as follows: O5, O6, O7, O8 > N3, N4 > N1, N2. However,   we noticed for these molecules that all carbon atoms of two aromatic rings have the same ability of electron-accepting character. This result is very changed for SSBO molecule, which presents low electrophilic sites (N1, N2 and carbon atoms of aromatic ring) and low nucleophilic sites (N3, N4, O5, O6, O7, O8, C9, C10 and C11). This confirms the previous results obtained by the analysis of the energy gap (ΔE inh-Fe ), HOMO/LUMO shapes and QTAIM calculations. The non-covalent intramolecular interactions of SSBs molecules were evaluated by the molecular NCI analysis (Fig. 13). As shown in Fig. 13, we observed important repulsive interactions in almost the entire SBBO structure, mainly at the level of active atoms N3 and N4 of 2,3-diaza group and O5, O6, O7, and O8 of nitro groups. The presence of these repulsive interactions renders difficult the adsorption of SSBO with the iron surface. As for SSBM structure, we observed a forte attractive interaction arises between oxygen atoms of nitro groups (O6 and O7) and their adjacent hydrogen atoms of two aromatic rings, which is a sufficient condition to form hydrogen bonds in these regions and offer high stability to the SSBM. In addition, we noticed that this structure presents any repulsive interactions around the 2,3-diaza and the nitro groups. However, the SSBP structure presents a few attractive interactions that are found between oxygen atoms of nitro groups (O6 and O8) and their adjacent hydrogen atoms of two aromatic rings. Furthermore, it is noticed that SSBP structure also presents repulsive interactions between hydrogen atoms of methyl groups and their neighboring hydrogen atoms of two aromatic rings, implies less reactivity of SSBP with iron atoms compared to that of SSBM structure. Further to the NCI analysis, the bond critical point (BCP) analysis was performed to evaluate strength related to the hydrogen bonds that appeared at SSBM and SSBP structures using QTAIM theory. In the context of this theory, the hydrogen bonds energy ( ) expressed as a function of potential energy density ( BCP ) at corresponding BCP described by the following equation (21) [43]: The corresponding values of V(r BCP ) related to the hydrogen bonds C benz -H⋯O6 and C benz -H⋯O7 for SSBM, and C benz -H⋯O6 and C benz -H⋯O8 for SSBP are regrouped in Table 8. From this Table, we noticed that the hydrogen bonds have more stability in the SSBM structure (lower value of ) than in SSBP (higher value of ); thus the stagnation of the electron density at oxygen atoms of nitro groups is more in SSBM than in SSBP, this result suggests that O-Fe interactions are more important in SSBM than in SSBP and SSBO.

Fe-complexation study
According to QTAIM and MASD results; we can propose for each inhibitor two possibilities of complexation with Fe metal. The first one is the coordination of oxygen atoms of nitro groups with Fe, and the second is the coordination of nitrogen atoms of 2,3-diaza group with Fe. The evaluating of relative free energy (Δ ), activation energy (Δ ) and localization of the transition states (TSs) for the proposed complexes (Fig. 14) were assessed using QST2 approach. Table 9 shows some theoretical parameters like free energy , relative free energy Δ and activation energy Δ calculated for all possible complexes structures. The Free energy profile of the Fe-complexation process is schematized in Fig. 15.
According to Table 9 and Fig. 15, we noticed that the complexation was found to be spontaneous (negative value of Δ ). Moreover, the SSBM complexes present the lowest values of Δ with respect to the other complexes. To this result, the thermodynamic stability of the concerned complexes can be abiding by the following trend: SSBM-complex > SSBP-complex > SSBO-complex. This indicates that SSBM has the greatest attachment and non-desorption to the iron surface with respect to the SSBP and SSBO. In addition, we noticed that the changing of nitro ortho-, meta-or para-group position causes an important change in the activation energy barrier, which are higher for SSBO and SSBP. This indicates that the coordination of SSBM with the iron surface is more kinetically favored (lower values of Δ ) than SSBO and SSBP. This could be attributed probably to the less/hindered obstruction entire the SSBM structure. The GEDT values calculated for TSs structures and their imaginary frequencies are gathered in Table 10. Therefore, the computed GEDT at the TSs (Fig. 14) is increased in the following order: (GEDT(TS-Fe@SSBM) > GEDT(TS-Fe@SSB) > GEDT(TS-Fe@SSB). As conclusion, free energy, activation energy and GEDT parameters exhibit the following trend of the inhibition efficiency for the studied inhibitors: SSBM > SSBP > SSBO. This is in good accordance with the trend obtained experimentally.
As for complex systems, the molecular NBO analysis was widely used to describe donor-acceptor interactions that occur between active sites of an organic molecule and metal by calculating the second-order stabilization energy E (2) and describing electronic configurations (EC) of active sites. In this present study, the E (2) parameter has been calculated for possible hyper-conjugative interactions that could be between  Table 8. Calculated potential energy density at BCP, V(r BCP ) in a.u., of studied hydrogen bonds (HBs) and their energy, E HB in kJ.mol −1 . for atoms Fe, N3, N4, O5, and O8 have been analyzed. EC and E (2) results are grouped in Table 10. Generally, a large value of E (2) means a more intensive donor-acceptor interaction which could be considered as a good representation of the bond strength. The results of Table 11 show that the range of E (2) values is 12.83 to 48.88 kcal.mol −1 , 22.34 to 84.51 kcal.mol −1 , and 19.00 to 74.92 kcal.mol −1 for SSBO, SSBM and SSBP, respectively. This result indicates that the strength of coordination of inhibitor molecule with iron atoms is in follow the trend: SSBM > SSBP > SSBO. Additionally, the CE results indicate clearly that the electron density transfer of adsorption takes place from nitrogen atoms (N3 and N4) of 2,3-diaza group and from oxygen atoms (O5 and O8) of nitro groups to the 3d-empty orbital of iron atoms. Electron den-sity transfer from the active site of inhibitor molecule to iron atoms has been enhanced as follows: SSBM > SSBP > SSBO, which is in good agreement with the trend of inhibition efficiency obtained through the experiment essays.

Protonation of inhibitors
The most nucleophilic sites of inhibitors such as N3, N4, O5 and O8 have great ability to be protonated in acidic media. This behavior was established from DFT calculations where the protonated inhibitor molecules possess lesser free energy than not protonated ones. In order to confirm possibility of protonation process of inhibitors, optimization of all possible protonated structures with different nucleophilic centers for protonation (Fig. 16) and calculating some energetic parameters were performed. Table 12 shows some theoretical parameters such as the free energy , relative free energy Δ and ΔE (inh-Fe) calculated for all possible protonated structures. The negative value of Δ showed the possibility of protonation process. Values of ΔE (inh-Fe) calculated for protonated inhibitors are lower than those obtained for not protonated inhibitors. This result suggests more ability of non-protonated inhibitor molecules to adsorb iron surface compared to the protonated inhibitors.

Strength of interfacial interaction
Molecular dynamics simulation was performed at temperature of 308 Kelvin until the studied interface reaches equilibrium. In this context, the most stable adsorption configurations of the not protonated molecules (SSBs) and the protonated ones (SSBH+) on Fe (110) surface are given in Fig. 17 and 18, respectively. Besides, the strength of  Table 9. B3LYP/6-311G+ +(2d,2p)/LanL2DZ free energy (G) and relative free energy (ΔG) and GD3-B3LYP/6-311G + +(2d,2p)/LanL2DZ for activation energies (Ga) of TSs leading to the corresponding complexes.  the interfacial interactions has generally been evaluated based on the adsorption energy ( ads ) or binding energy ( binding ) and desorption energy ( ads / inh ). Binding energy is defined as the opposite of adsorption energy as follows (22) [33]: In addition, ads / inh is the energy required to remove an adsorbate from the iron surface (110), a high value of ads / inh due to the strong adsorption of the inhibitor on the iron surface (110) [10,44]. The high value of the binding energy (or high absolute value of the adsorption energy) reproduces strong adsorption behavior. The different values of the energies are calculated in the solution containing the inhibitor, 500 molecules of water, 20 oxonium ions (H 3 O + ), and 20 chlorine ions Cl − and reported in Table 13. From the careful observation of Fig. 17 it can be said that the molecules SSBM and SSBP adsorb in large part on the iron surface, which demonstrates that these molecules have a high tendency to form a dense film entire iron surface and consequently promoting the protection of C38 steel against corrosion in the 1M HCl solution. However, the adsorption of SSBO is happening in a part consisting of nitrogen dioxide and the phenyl double bond, while the rest of the molecule is taking a sloping form on the surface solution. Additionally, these observations confirm the high inhibitory efficiency of SSBM and SSBP due to the more active site over molecule structures of these inhibitors. As for the protonated forms of inhibitors (Fig. 18), we observed that all protonated inhibitors are not oriented appropriately above the iron surface, and thus leads to the low coverage of these molecule structures onto the iron surface. These re-sults allow us to conclude that the anti-corrosive property is favorable when the inhibitors studied were at their neutral forms (non-protonated forms). Furthermore, as shown in the Table 13, the negative values of ads mean that the studied adsorption is spontaneously shaped and thus, the inhibitor has qualitatively a high adsorption capability to interact with the iron surface [10,44]. Moreover, we noticed that the binding energy ( binding ) related to the adsorption of inhibitors on Fe (110) surface increased in the following order: SSBO/Fe (110) < SSBP/Fe (110) < SSBM/Fe (110). This is in good agreement with the trend of inhibitory efficiency found in the electrochemical and quantum studies sections. This observation is strengthened by the comparison of the values of desorption energies that shows the following trend: ads /dNi (SSBM) > ads /dNi (SSBP) > ads /dNi (SSBO). This difference could be explained by the fact that SSBM and SSBP present less hindered/steric obstruction which gives them a high coverage entire iron surface. For the protonated forms, we noticed a strong decrease in both binding energy and desorption energies (Table 13). This result indicates lower adsorption of SSBH+ on the iron surface than SSBs in 1M HCl. The results obtained were supported by other calculations discussed below based on the pair atomic distribution function (PADF), mean square displacement (MSD) and free volume fraction (FVF) [33,41,45].

PADF calculations
The pair atomic distribution function (PADF) theory, so-called g(r) function, is most commonly used to describe how the electron density between the atoms of a molecule and iron surface varies with distance from an infinitesimal distance r+dr. This theory gives information about the probability with which certain inter-atomic distances between atoms X and Y [33]. The g(r) is defined as the ratio of the local density of "Y" at a distance r from "Y" particles by the following equation (23): where ⟨ ⟩ local represents the average local number density of "Y" particles over all layers which surround the "X" particle. In general, if the distance values between X and Y atoms include the range [1-3.5 Å], strong connections are present (i.e. chemical bonds). If the contrary, there are weak connections (i.e. physical bonds) [33]. Fig. 19 shows the variation of PADF versus the bond lengths (r) such as Fe-N3, Fe-N4, Fe-O5, and Fe-O8 for SSBs and SSBH+. For the nonprotonated forms of inhibitors (Fig. 19a), we observed the appearance  of peaks with distances < 3.5 Å and the others with distances > 3.5 Å. This result indicates that SSBO, SSBM, SSBP coordinate to Fe (110) surface through both chemical and physical bonds. While, for the proto-  nated forms of inhibitors (Fig. 19b), it is clearly remarked that all peaks have appeared at distances > 3.5 Å; indicating the presence of weak connections between SSBH + and iron surface. To these results, we concluded that adsorption of inhibitors onto the iron surface is mixed-type (chemisorption and physisorption), and the non-protonated structures of the inhibitor are dominated in the adsorption than the protonated ones.

MSD calculations
The mean square displacement (MSD) curves and the diffusion coefficient (D) behavior of corrosive ions (3H 3 O + and 3Cl − ) in the supercell that covers 30 molecules of each inhibitor (protonated or nonprotonated one) were modeled through Einstein equations (24) and (25), respectively [45]. MSD and diffusion coefficient calculations for SSBs and SSBH + are shown in Fig. 20 and 21, respectively.
where represents the number of corrosive ions, whereas ( ) and (0) are the displacement of the corrosive ion between moment t and the initial moment t 0 respectively. The diffusion coefficient can be calculated through MSD curves using the following equation (26) [45,46]: where the m is the slope of MSD curve. Furthermore, it is noted that a low diffusion coefficient (D) value reflects high corrosion inhibition efficiency. The D values are concluded from the RMS curves gathered in Fig. 20 and 21. According to these figures, the D values for H 3 O + are 0.00454 × 10 12 , 0.00179 × 10 12 , and 0.00255 × 10 12 m 2 /s for SSBO, SSBM and SSBP molecules, respectively. However for Cl − the D values are 0.00423 × 10 12 , 0.00219 × 10 12 , and 0.00229 × 10 12 m 2 /s for SSBO, SSBM and SSBP molecules, respectively. Moreover, the D values of Cl − ions are 0.00290 × 10 12 , 0.00223 × 10 12 , and 0.00254 × 10 12 m 2 /s for SS-BOH+, SSBMH + and SSBPH +, respectively. Then, for H 3 O + ions the D values are 0.00572 × 10 12 , 0.00337 × 10 12 , and 0.00381 × 10 12 m 2 /s for SSBOH +, SSBMH + and SSBPH +, respectively. These findings suggest the best inhibition efficiency of SSBM (low value of D) than SSBO and SSBP, which is in good agreement with all results discussed above.

FFV calculations
Further, the evaluation of free volume inside each inhibitor was performed by molecular dynamics simulation. Based on the outputted results of MDS, the free fractional volume (FFV), is calculated using the following equation (27) [45,46,47]: where V free is the free volume and V occ is the volume occupied by the inhibitor film on the CS surface. V free is concluded as given by the following equation (28) [47]: = where E free is the free energy density, R is the universal gas constant, T is the temperature, and P is the atmospheric pressure. H3O + and Cl − ions were chosen as probe particles (sphere radii 2 nm and bead diffusion coefficient e −7 cm 2 /s). Evidently, a large value of FFV means  that there are abundant voids over inhibition film, and the movement probability of corrosive species is high, which makes to low inhibition efficiency. While, a small value of FFV induces to high inhibition efficiency of corrosion [45,46]. As shown in Fig. 22, the molecular graphic showing the free volume distribution (blue and red regions) through an amorphous cell contains 15 inhibitors, 2H 3 O + and 2Cl − . Indeed, red color indicates high free energy density (i.e., low free volume), the blue color indicates low free energy (i.e. high free volume), and green color represents the occupied volume by inhibitor molecules [48]. The free volume distributions and FFV values for SSBs molecules are given in Fig. 22. Indeed, the present FFV values calculated for SSBO, SSBM and SSBP are 29.64, 11.78 and 14.12%, respectively. This observation reveals that the addition of SSBs molecules into the corrosive environment creates a barrier film on the CS surface and limits migration of corrosive species, which is in the following order: SSBM > SSBP > SSBO. This result further reinforces the high inhibition performance of SSBM than SSBO and SSBP and supports all results discussed previously in this work.

Inhibitive corrosion mechanism
From the results discussed above, the safeguarding of C38 steel by the presence of SSBs inhibitors depends on the higher electron density clouds around the nucleophilic atoms (N3, N4, O5 and O8), the electrons of 2,3-diaza/nitro groups and lone-pair electrons of nitrogen and oxygen atoms (N3, N4, O5 and O8) available on SSBs molecules, which shared with d-empty orbitals of CS to form a protective layer against corrosion. Additionally, the SSBs molecules are adsorbed electrostatically onto the anions enclosed CS surface via its protonated form. The inhibitive corrosion mechanism is illustrated in Fig. 23. The order of the inhibitory efficiency for SSBs molecules where the nitro group places in ortho-(SBBO/NO2-ortho), meta-(SSBM/NO2-meta) or para-(SSBP/NO2-para) positions is illustrated in Fig. 24.
A comparison of inhibition efficiency (%) with similar organic compounds shows the higher inhibitive performance of our tested in-hibitors; in particular, SSBM can be considered a promising candidate for corrosion inhibition of C38 steel in acidic media (Table 14).

Conclusion
In this study, three hydrazine derivatives SSBO, SSBM, and SSBP have been effectively explored as cost-effective and eco-friendly inhibitors against corrosion of C38 steel in 1M HCl solution. The concluded results are mentioned below: • The inhibition efficiency is improved when the inhibitor concentration increased to reach a maximum of 85.32, 88.42% and 93.04, at 1 mM for SSBO, SSBP and SSBM, respectively; • The PDP measurements indicated that SSBs were a mixed-type inhibitor with a predominantly cathodic control;  • The EIS results showed that there are two capacitive loops. The first at high frequencies was attributed to the inhibitor film and the second was related to the charge transfer phenomenon; • The adsorption isotherm study showed that the tested inhibitors obeyed the Langmuir adsorption isotherm and the ΔG ads values suggested that these inhibitors acted through a chemisorption process; • The protective effect of SSBs was confirmed using SEM-EDS test and element mapping analysis; • Experimental results were successfully elucidated based on quantum chemical calculations; • Molecular dynamics simulation showed clearly that the inhibitive performance is better for the not protonated inhibitor molecules than protonated ones; • The inhibition efficiency is strongly depending on both the electronic structure and the nature of the geometry of the assayed compounds.